In recent years, coherent optical detection (E. Ip and J. M. Kahn, “Fiber Impairment Compensation Using Coherent Detection and Digital Signal Processing,” J. Light. Technol., vol. 28, no. 4, pp. 502-519, Feb. 2010) has been deployed on a large scale for high-speed long-haul optical transmission. Despite substantial performance advantages, the complexity and power consumption of coherent optical receivers are prohibitive, precluding their usage in cost-sensitive short-reach applications such as data-centers and their interconnects, as well as optical access networks such as passive optical networks. Currently coherent optical receivers are mainly used in long-haul and regional metro transmission but are uneconomic for cost-sensitive optical communication at short distances (<100 km). The search continues for high-capacity optical transmission methods at short reach, which are “coherent-like”, sharing many of the performance advantages of coherent detection, yet at lower complexity, cost and power consumption.